1. Technical Field
The present disclosure relates to image reconstruction and, more specifically, to compressed sensing reconstruction using context information.
2. Discussion of Related Art
In magnetic resonance imaging (MRI), internal structures of patients' bodies may be imaged by reconstructing magnetic resonance data. As the magnetic resonance data may be acquired in a sensing domain, for example, a Fourier domain, reconstruction of the acquired data may involve a transformation into an image domain, for example, using an inverse Fourier transformation.
Image acquisition may be performed under time-sensitive conditions to ensure that there is no movement of the subject during the image acquisition process. Thus, image acquisition may be performed while the patient refrains from moving. Often this requires the patient holding breath. Where the MRI study seeks to track motion such as cardiac motion, acquisition time might have to be especially short.
In light of this shortened acquisition time, it may be difficult to acquire data at the Nyquist rate to ensure sufficient sampling for ideal image reconstruction. Accordingly, performing accurate reconstruction with less than an ideal amount of data may be difficult. This difficulty in reconstructing an image under these conditions may be similar to trying to solve for a system of linear equations in which there are more unknown variables then there are equations. In such a case, there may be an infinite number of possible solutions.
Compressed sensing (CS) techniques have been developed to aid in reconstructing a signal using a sampling rate that is below the Nyquist sampling rate. These techniques exploit the observation that most practical signals of interest have sparse representations using a specific transform. Thus, for a given signal, there may exist a particular transformation space in which a majority of the transform coefficients are at or near zero. This transformation space may be referred to as the sparsity space. As these small coefficients may be assumed to be zero without significant loss of signal quality (the sparseness assumption), signal reconstruction may be approximated by determining only the limited set of large transform coefficients for the sparsity space. When dealing with image reconstruction of MRI signals, a wavelet transform space may serve as an effective sparsity space.
Accordingly, when using CS techniques, transform coefficients may be determined from limited available data by seeking a solution that maximizes sparsity while conforming to the available data. Thus, the signal is reconstructed by finding the sparsest solution from among the infinitely many candidates satisfying the available measurements.
While existing CS techniques may be helpful in reconstructing images from limited available data, new techniques are desired that can be used to produce reconstructed images with superior image quality and increased signal-to-noise ratios in less time than current CS techniques permit.